Problem: Ben is 3 times as old as Nadia. Twenty years ago, Ben was 8 times as old as Nadia. How old is Nadia now?
Explanation: We can use the given information to write down two equations that describe the ages of Ben and Nadia. Let Ben's current age be $b$ and Nadia's current age be $n$ The information in the first sentence can be expressed in the following equation: $b = 3n$ Twenty years ago, Ben was $b - 20$ years old, and Nadia was $n - 20$ years old. The information in the second sentence can be expressed in the following equation: $b - 20 = 8(n - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to use our first equation for $b$ and substitute it into our second equation. Our first equation is: $b = 3n$ . Substituting this into our second equation, we get: $3n$ $-$ $20 = 8(n - 20)$ which combines the information about $n$ from both of our original equations. Simplifying the right side of this equation, we get: $3 n - 20 = 8 n - 160$ Solving for $n$ , we get: $5 n = 140.$ $n = 28$.